When putting Youtube videos on a page where the Youtube video was near the top, I was having an issue where the drop down menu would go behind the video. Here is the code to properly put a youtube video on your Joomla page and to ensure that the menu is on top. The key is the wmode="transparent"
<p style="text-align: center;"><embed type="application/x-shockwave-flash" width="425" height="344" src="http://www.youtube.com/v/VIDEOLETTERSHERE&hl=en_US&fs=1" wmode="transparent" allowscriptaccess="always" allowfullscreen="true"></embed></p>
Note: You'll want to adjust the width, height, and VIDEOLETTERSHERE to correspond to your youtube video.